Singular Dirichlet problem for ordinary differential equation with impulses

Nonlinear Analysis, Theory, Methods and Applications

Volumn 65, Issue 1, 2006, Pages 210-229

  Rachůnková, Irena ^a   Tomeček, Jan ^a  

^a PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

Dirichlet conditions; Impulses; Lower and upper functions; Singular ordinary differential equation of the second order; Time singularities

Indexed keywords

CONTROL SYSTEMS; NUMERICAL METHODS; PARAMETER ESTIMATION; PROBLEM SOLVING; THEOREM PROVING;

DIRICHLET CONDITIONS; IMPULSES; LOWER AND UPPER FUNCTIONS; SINGULAR ORDINARY DIFFERENTIAL EQUATION OF THE SECOND ORDER; TIME SINGULARITIES;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 33646156421     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.09.016     Document Type: Article

References (34)

1. Agarwal R.P., and O'Regan D. Multiple nonnegative solutions for second order impulsive differential equations. Appl. Math. Comput. 114 (2000) 51-59
2. Asakawa H. Nonresonant singular two-point boundary value problem. Nonlinear Anal. 44 (2001) 791-809
3. J.V. Baxley, Numerical solution of singular nonlinear boundary value problems, D. Bainov, V. Covachev (Eds.), Proceedings of the Third International Colloquium in Numerical Analysis, VSP BV, Plovdiv, Bulgaria, 1995, pp. 15-24.
4. Baxley J.V., and Thompson H.B. Boundary behavior and computation of solutions of singular nonlinear boundary value problems. Commun. Appl. Anal. 4 (2004) 207-226
5. R.E. Bellman, Topics in pharmacokinetics, III: repeated dosage and impulse control, Math. Biosci. 12(1-2) (1971), J. Math. Anal. Appl. 184 (1994) 263-284.
6. Blaguiere A. Differential games with piecewise continuous trajectories. In: Hagedorn P., Knobloch H.W., and Olsder G.J. (Eds). Differential Games and Applications (1977), Springer, Berlin
7. Bobisud L.E., and O'Regan D. Positive solutions for a class of nonlinear singular boundary value problems at resonance. J. Math. Anal. Appl. 184 (1994) 263-284
8. Callegari A., and Nachman A. Some singular, nonlinear differential equations arising in boundary layer theory. J. Math. Anal. Appl. 64 (1978) 96-105
9. Callegari A., and Nachman A. A nonlinear singular boundary value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math. 38 (1980) 275-281
10. Doddaballapur V., Eloe P.W., and Zhang Y. Quadratic convergence of approximate solutions of two-point boundary value problems with impulse. Electron. J. Differential Equations Conf. 01 (1997) 81-95
11. Eloe P.W., and Henderson J. Positive solutions of boundary value problems for ordinary differential equations with impulse. Dyn. Contin. Discrete Impulsive Syst. 4 (1998) 285-294
12. Erbe L.H., and Liu X. Existence results for boundary value problems of second order impulsive differential equations. J. Math. Anal. Appl. 149 (1990) 56-69
13. Gatica J.A., and Waltman P. A threshold model of antigen antibody dynamics with fading memory. In: Lakshmikantham V. (Ed). Nonlinear Phenomena in Mathematical Science (1982), Academic Press, New York
14. Gorbunov V.K. Differential-impulsive games. Izv. Acad. Nauk SSSR, Tekh. Kibern. 4 (1973) 80-84
15. Habets P., and Zanolin F. Upper and lower solutions for a generalized Emden-Fowler equation. J. Math. Anal. Appl. 181 (1994) 684-700
16. Kalitin B.S. On pendulum oscillations with a shock impulse. Differential'nye Uravneniya 6 (1970) 2174-2181
17. Kiguradze I. Some Singular Boundary Value Problems for Ordinary Differential Equations (1975), ITU, Tbilisi (in Russian)
18. Kiguradze I. Some optimal conditions for the solvability of two-point singular boundary value problems. Funct. Differential Equations 10 (2003) 259-281
19. Kiguradze I.T., and Shekhter B.L. Singular boundary-value problems for ordinary second-order differential equations. Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Novejshie Dostizh. 30 (1987) 105-201 (in Russian)
20. Kruger-Thiemer E. Formal theory of drug dosage regiments. I, J. Theor. Biol. 13 (1966)
21. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
22. Lepin A., and Ponomarev V. On a singular boundary value problem for a second order ordinary differential equation. Nonlinear Anal. 42 (2000) 949-960
23. Lomtatidze A., and Malaguti L. On a two-point boundary value problem for the second order ordinary differential equations with singularities. Nonlinear Anal. 52 (2003) 1553-1567
24. O'Regan D. Theory of Singular Boundary Value Problems (1994), World Scientific, London
25. O'Regan D. Singular Dirichlet boundary value problems - I. Superlinear and nonresonant case. Nonlinear Anal., Theory Methods Appl. 29 (1997) 221-245
26. O'Regan D. Singular Dirichlet boundary value problems II: resonance case. Czech. Math. J. 48 (1998)
27. Rachůnková I., and Tomeček J. Impulsive BVPs with nonlinear boundary conditions for the second order differential equations without growth restrictions. J. Math. Anal. Appl. 292 (2004) 525-539
28. Samoilenko A.M., and Perestyuk A. Impulsive Differential Equations (1995), World Scientific, Singapore
29. Xu X. Positive solutions of generalized Emden-Fowler equation. Nonlinear Anal. 53 (2003) 23-44
30. Xu X. Existence of multiple positive solutions for singular impulsive boundary value problems in Banach spaces. Northeast. Math. J. 20 (2004) 317-330
31. Zhang Y. Positive solutions of singular sublinear Emden-Fowler boundary value problems. J. Math. Anal. Appl. 185 (1994) 215-222
32. R.P. Agarwal, D. Franco, D. O'Regan, Singular boundary value problems for first and second order impulsive differential equations, Aequationes Math. 69 (2005) 83-96.
33. I. Rachůnková, Singular Dirichlet second-order BVPs with impulses, J. Differential Equations 193 (2003) 435-459.
34. X. Xu, Multiple solutions of singular impulsive boundary value problem with polynomial nonlinearity. Advances in impulsive differential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 9 (2002) 353-365.